Fall 2003Math 151COMMON EXAM IITest Form APRINT: Last Name: First Name:Signature: ID:Instructor’s Name: Section #Instructor use only.Multiple choiceQ12Q13Q14Q15Q16Q17Q18TotalINSTRUCTIONS1. In Part 1 (Problems 1–11), mark the correct choice on your ScanTron form usinga #2 pencil. For your own records, also record your choices on your exam! TheScanTrons will be collected after 1 hour; they will NOT be returned.2. In Part 2 (Problems 12–18), write all solutions in the space provided. All workto be graded must be shown in the space provided. CLEARLY INDICATE YOURFINAL ANSWERS.1PART 1: MULTIPLE-CHOICE PROBLEMSEach problem is worth 4 points: NO partial credit will be given. Calculators may NOT be used on thispart. ScanTron forms will be collected after 1 hour.1. If p(x)=x3−12x1/2+9,thenp0(4) =(a) 25(b) 45(c) 49(d) 50(e) 542. Let f(x)=g(x)h(x)and suppose g(2) = 6,g0(2) = −1, h(2) = 3, h0(2) = 4.Thenf0(2) =(a) −3(b) −14(c)14(d) 7/3(e) 33. Let f be the function defined by f(x)=(x−1)(x +3)x2−1. Find the vertical and horizontal asymptotes of thegraph of f .(a) vertical asymptote x = −1; horizontal asymptote y =1(b) vertical asymptotes x = −1, x =1; horizontal asymptote y =1(c) vertical asymptotes x = −1, x =1; horizontal asymptote y =0(d) vertical asymptote x = −1; horizontal asymptote y =0(e) vertical asymptotes x = −1, x =1; horizontal asymptotes y =1,y=34. A moving object’s position at time t is given by the vector functionrrr(t)=(t2−t)iii+(4−3t+4t2)jjj.Find the instantaneous velocity of the object when t =2.a) 3iii +13jjjb) 2iii +14jjjc) 4iii +14jjjd) 13iii − 57jjje) none of these25. A line L is the graph of the vector functionrrr(t)=h2+6t, −3+4ti.The slope of L is(a) 6(b) 4(c) −32(d)32(e)236. The constant force FFF = −2iii +3jjjmoves an object along the straight line from the point (−1, 5) to the point(4,9). Find the work done if distance is in meters, force in Newtons(a) 3 N · m(b)√41(−2iii +3jjj) N·m(c)√41 N · m(d) 2 N · m(e) 2(−2 iii +3jjj) N·m7. The displacement of a particle moving in a straight line is given by s =6+8t2−t44,wheretis time inseconds and distance is in meters. What is the average velocity of the particle over the time interval [0,2]?(a) −24 m/s(b) −14 m/s(c) 0 m/s(d) 14 m/s(e) 24 m/s8. Which of the following is true about limx→3−|x − 3|x2− 9?(a) The limit does not exist(b) The limit is ∞(c) The limit is16(d) The limit is −16(e) The limit is 09. The domain of the function f defined by f (x)=√x2−6xis(a) all real numbers(b) all numbers except 0 and 6(c) {x | x ≥ 6}(d) {x | 0 ≤ x ≤ 6}(e) {x | x ≤ 0 or x ≥ 6}310. Evaluate limx→4x −4x2− x − 12.(a) 0(b)17(c)13(d) 1(e) ∞11. Which of the following is a unit vector orthogonal to h3, 4i?(a) h−4, 3i(b) h4, 3i(c) .8 iii + .6jjj(d) .8 iii −.6jjj(e) none of these.4PART 2: WORK-OUT PROBLEMSEach problem is worth 8 points; partial credit is possible. Calculators may NOT be used on this part. SHOW ALLWORK!12. (a) (3 points) Write the definition of the derivative of a function f at a number c.(b) (5 points) Use the definition of the derivative to calculate the derivative of f (x)=√2−xat x =1.13. (a) (4 points) Find the scalar projection of 4iii +2jjjonto iii − 3jjj.(b) (4 points) Find the vector projection of 4iii +2jjjonto iii − 3jjj.514. Find an equation for the tangent line to the curve y =2x3−5x2+6at the point where x =1.15. (a) (4 points) Differentiate: f(x)=3x+62x2−4x(b) (4 points) Differentiate: g(x)=(4−6x+7x2)(2x −x3+ x4)16. Evaluate limx→∞(√x2+3x−x).617. Find the value of the constant c that makes the function f (x)=x2−1 if x<32cx if x ≥ 3continuous on (−∞, ∞).Clearly EXPLAIN your answer!18. Good writing is expected in this problem.(a) (4 points) State the Intermediate Value Theorem.(b) (4 points) Use the Intermediate Value Theorem to explain why the equation x3− x − 1=0has a rootbetween 1 and
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